In-plane and anti-plane strong shaking of soil systems and structures G. Gudehus, R.O. Cudmani * , A.B. Libreros-Bertini, M.M. Bu ¨hler Institute of Soil Mechanics and Rock Mechanics, Faculty of Civil Engineering, University of Karlsruhe, Postfach 6980, Engler-Bunte-Ring 14, 76128 Karlsruhe, Germany Accepted 11 December 2003 Abstract The concept of in-plane and anti-plane shaking is introduced with a rigid block on a plane surface with Coulomb friction. Using a hypoplastic constitutive relation to model the mechanical behaviour of the soil, numerical solutions for a rigid block on a thin dry or saturated soil layer are obtained. The coupled nature of dynamic problems involving granular materials is shown, i.e. the motion of the block changes the soil state—skeleton stresses and density—which in turn affects the block motion. Motions of the block as well as soil response can be more realistically calculated by the new model. The same constitutive equation is applied to the numerical simulation of the propagation of plane waves in homogeneous and layered level soil deposits induced by a wave coming from below. Experiments with a novel laminar shake box as well as real seismic records from well-documented sites during strong earthquakes are used to verify the adequacy of the hypoplasticity-based numerical model for the prediction of soil response during strong earthquakes. The response of a homogeneous earth dam subjected to in-plane and anti-plane shaking is investigated numerically. In-plane and anti-plane shaking is shown to cause nearly the same spreading of a sand dam under drained conditions, whereas under undrained conditions anti-plane shaking causes stronger spreading of the dam. The dynamic behaviour of a breakwater founded on rockfill and soft clay during the 1995 Kobe earthquake is back-calculated to show the good performance of the proposed numerical model also with a structure. Section 9 deals with buildings on mattresses of densified cohesionless soils or fine-grained soils with granular columns, slopes with ‘hidden’ dams and structures on piles traversing clayey slopes to show the suitability of hypoplasticity-based models for the earthquake-resistant design and safety assessment of geotechnical systems. q 2004 Elsevier Ltd. All rights reserved. Keywords: Seismic soil response; Non-linear wave propagation; Soil liquefaction; Finite element modelling; Hypoplasticity; Dynamic soil–structure interaction 1. Introduction The M 7.2 Gujarat earthquake 2001 caused severe damage in the Indian harbour Kandla [30]. The direction of shaking was parallel to the shoreline, i.e. it was anti-plane with respect to the cross-section of the pier. For this reason, conventional methods for the assessment of stability and serviceability of geotechnical structures which assume in- plane shaking [16] were not able to predict the observed damage. A similar statement can be made for the Port and Rocco Islands in Kobe. During the M 6.9 Hyogoken– Nambu earthquake 1995 their rims spreaded rather independently of their direction, whereas the major inner parts experienced a rather uniform settlement and almost no damage. The necessity of a thorough revision of conventional methods has also been corroborated by the damage caused by the M 7.1 Aigio earthquake 1995 in Greece. Parts of the shore slid seawards independently of their direction, damaging severely buildings located at the coast, whereas buildings in the coastal flatland remained undamaged. This happened several times and has shaped the landscape and its use [7,9]. The Newmark method [20], which assumes a rigid block sliding, is often used for estimation of displacements due to ground shaking. Newmark’s solution can be shown (Section 2) to be on the safe side for ground shaking in the direction of the incline (in-plane), but not for a shaking perpendicular to it (anti-plane). The usually performed ground response analysis assumes linear visco-elastic or pseudo-visco-elastic soil behaviour. The latter considers a degradation of the shear modulus and an increase of damping with increasing shear deformation in a very 0267-7261/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.soildyn.2003.12.007 Soil Dynamics and Earthquake Engineering 24 (2004) 319–342 www.elsevier.com/locate/soildyn * Corresponding author. E-mail address: roberto.cudmani@ibf.uni-karlsruhe.de (R.O. Cudmani).